Modified quadratic residue constructions and new extremal binary self-dual codes of lengths 64, 66 and 68

被引：5

作者：

Gildea, Joe ^{[1
]}

Hamilton, Holly ^{[1
]}

Kaya, Abidin ^{[2
]}

Yildiz, Bahattin ^{[3
]}

机构：

[1] Univ Chester, Fac Sci & Engn, Dept Math, Chester, Cheshire, England

[2] Sampoerna Univ, Dept Math Educ, Jakarta 12780, Indonesia

[3] No Arizona Univ, Dept Math & Stat, Flagstaff, AZ 86001 USA

来源：

INFORMATION PROCESSING LETTERS | 2020年 / 157卷

关键词：

Combinatorial problems; Extremal self-dual codes; Codes over rings; Quadratic residues; Quadratic circulant matrices; II CODES;

D O I：

10.1016/j.ipl.2020.105927

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this work we consider modified versions of quadratic double circulant and quadratic bordered double circulant constructions over the binary field and the rings F-2 + uF(2) and F-4 + uF(4) for different prime values of p. Using these constructions with extensions and neighbors we are able to construct a number of extremal binary self-dual codes of different lengths with new parameters in their weight enumerators. In particular we construct 2 new codes of length 64, 4 new codes of length 66 and 14 new codes of length 68. The binary generator matrices of the new codes are available online at [8]. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：8

共 50 条

[1] Extremal self-dual codes of lengths 66 and 68
Tsai, HP
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1999, 45 (06) : 2129 - 2133
[2] NEW EXTREMAL BINARY SELF-DUAL CODES OF LENGTHS 66 AND 68 FROM CODES OVER Rk,m
Kaya, Abidin
Tufekci, Nesibe
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2017, 54 (01) : 29 - 42
[3] New extremal binary self-dual codes of lengths 64 and 66 from R2-lifts
Kaya, Abidin
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2017, 46 : 271 - 279
[4] COMPOSITE CONSTRUCTIONS OF SELF-DUAL CODES FROM GROUP RINGS AND NEW EXTREMAL SELF-DUAL BINARY CODES OF LENGTH 68
Dougherty, Steven T.
Gildea, Joe
Korban, Adrian
Kaya, Abidin
[J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2020, 14 (04) : 677 - 702
[5] Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes
Dougherty, Steven T.
Gildea, Joseph
Korban, Adrian
Kaya, Abidin
Tylyshchak, Alexander
Yildiz, Bahattin
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2019, 57 : 108 - 127
[6] New extremal binary self-dual codes of length 66 as extensions of self-dual codes over Rk
Karadeniz, Suat
Yildiz, Bahattin
[J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2013, 350 (08): : 1963 - 1973
[7] The binary extremal self-dual codes of lengths 38 and 40
Hyun Jin Kim
[J]. Designs, Codes and Cryptography, 2012, 63 : 43 - 57
[8] The binary extremal self-dual codes of lengths 38 and 40
Kim, Hyun Jin
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2012, 63 (01) : 43 - 57
[9] Extremal Binary Self-Dual Codes of Lengths 64 and 66 from Four-Circulant Constructions over F2 + uF2
Karadeniz, Suat
Yildiz, Bahattin
Aydin, Nuh
[J]. FILOMAT, 2014, 28 (05) : 937 - 945
[10] NEW EXTREMAL BINARY SELF-DUAL CODES OF LENGTH 68 FROM R2-LIFTS OF BINARY SELF-DUAL CODES
Karadeniz, Suat
Yildiz, Bahattin
[J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2013, 7 (02) : 219 - 229

← 1 2 3 4 5 →